月曜日, 4月 15, 2019

Keen & Chapman 2005 Profit in a dynamic model of the Circuit Hic Rhodus, Hic Salta! Profit in a dynamic model of the Monetary Circuit

Keen & Chapman 2005  Profit in a  dynamic model of the Circuit Hic Rhodus, Hic Salta! Profit in a dynamic model of the Monetary Circuit Steve Keen, University of  Western Sydney Brian Chapman, Monash Universityi Graziani’s simple but profound insight that “A true monetary economy  must therefore be using a token money” (Graziani 1989: 3) was  undoubtedly a major advance in the development of the monetary theory  of production. But attempts to go beyond it have raised a new dilemma that in many ways parallels the paradox of surplus value solved by Marx one and a half centuries ago.  It is the paradox of  monetary profit: how can capitalists borrow money, repay it with  interest, and still make a profit? Graziani provided a static  equilibrium formula for profits (Graziani 1989: 14), but this was effectively derived from  Kaleckian identities, and  not  integrated  with the model of  the circuit itself. Subsequent attempts to  solve the paradox within the  context of  the circuit have concluded that profit is a  “zero sum gain”: profit earned by one capitalist must  be at the expense of someone else—be it  worker, other capitalist, or banker. Rochon (2005) provided a thoughtful survey of the  literature, starting from  the proposition that The existence of monetary  profits at the macroeconomic level has always been a conundrum  for theoreticians  of  the monetary circuit… not only are firms unable to create profits, they also cannot raise  sufficient funds to cover the payment of interest. In other words, how can  M  become  M`?  (125).  In concluding  that all extant attempts to  answer this question were unsatisfactory, Rochon also, in our opinion, took the first step towards a solution. Though he commenced with the proposition  that “simplification  requires us  to  deal with a single circuit” (127), ultimately he concluded that while firms need to reimburse their working  capital at  the  end of  a  given period of production, they typically reimburse the investment over several periods of production. Indeed, firms often  take years to pay back an initial investment. We can claim,  therefore,  that the investment circuit is multiperiod… Hence, profits are formed because incomes equaling the value of working and  fixed capital are created,  while only a portion of the fixed capital needs to be reimbursed in any period. (135) Rochon’s insight is that solving the paradox  of profit requires breaking free of the distinction between “single period analysis” and “continuation analysis”, which has been one of the major axes of dispute between  endogenous money theorists. As Fontana puts it, “horizontalists” have relied upon single  period analysis, while  “structuralists”  have emphasized “a continuation theory of endogenous money” (Fontana 2004: 378). The trap of segmented time The concept of dividing time into periods during which expectations remain constant, linked to other single  periods with different (but also constant) expectations, has an obvious familiarity  to  economists who, though they are non-neoclassical themselves, 1 of 20 

were trained in the Marshallian concepts of the short and long run. It  also has an appeal of apparent simplicity, as Fontana put it: "A single-period theory of money is to be used as a simple device to separate out the effect of constant expectations  from  the effects of disappointment and changes in the state of expectations.” (Fontana 2004: 83) However, there is a trap in this beguiling simplicity, as Fontana acknowledged. If “horizontalists” treat each single period as being in equilibrium, all disequilibrium  change has to occur between periods—and effectively,  out of time.  With equilibrium  analysis explaining the situation during each period,  it  appears that successive  periods can only be linked via comparative statics. On the other hand, “continuation analysis”  seems to beset “structuralists” with overwhelming complexity, since expectations—and everything else—are changing continuously. Often this has resulted, as Fontana observed, in “the practical need for structuralists  to often rely on comparative statics exercises rather than full-blown dynamic experiments” (Fontana 2004: 381). Whichever way Circuitists turn, comparative statics seems inescapable. The solution, we argue, is to abandon the distinction itself, and instead to seek to combine in one analysis the horizontalist desire  for analytic  rigor,  and the structuralist emphasis on processes of change. We  achieve the latter by modeling the Circuit in continuous time  using differential equations, and the former by starting with the simplest possible level of  analysis, deliberately omitting consideration of  behavioral  issues, expectations  (fulfilled or  dashed), uncertainty, etc. We anticipate criticism that, by omitting these issues,  our analysis is nonKeynesian. We concur that a full-blown Circuitist model must include expectations  and uncertainty. However, until such time as Circuitists can explain the existence of  profits in a capitalist economy, Circuitist analysis is not merely non-Keynesian, it is not even an analysis of capitalism  itself. Once the basic analysis explains  what we perceive in the real world—the long-term  perpetuation of monetary production—then we can move on to the signature issues of Post Keynesian analysis. Modeling the Circuit in continuous time We consider a pure credit economy with capitalists, bankers and workers, but no central bank.1  The circuit begins with bankers extending loans to capitalists that  enable them  to hire workers, buy intermediate goods, produce and sell output.2 Loans necessarily include the obligations  to pay interest and repay principal. While loan contracts can take many forms, we model an intermediate form  that is also the aggregate outcome of many different loan contracts of  different terms in a multi-agent economy. Given an initial loan level of  KD(0), by the time  T  capitalists  will attempt to 1  However, the  framework  we  construct  can  serve  as a  basis for introducing  fiat  money  at  a later stage. 2We  use  plurals throughout  because  our  model aggregates the outcome of  multiple  agents, without at this  stage considering dynamics between  agents  of  the same  type. 

reduce the debt outstanding to the proportion X of its original level, where  X<1.This gives us the basic relation: = KTK X () ()0 DD  (1) We take the rate of interest on debt  rd  p.a.  as  fixed, and  likewise the rate of interest on positive account balances  of  rc, where  cd rr < . We  assume  that capitalists attempt to meet their  principal and interest  repayment obligations by paying  a fixed proportion  R  p.a.  of the outstanding debt. Part of  R  reflects repayment of the principal only;3  we label this  RP. Part reflects repayment of the interest on the debt, and is identical to  the amount added to debt by  banks under the loan contract. We spell these out here for the sake of clarity,  even though the two terms cancel each other out. Recording debt as a positive number,  so that interest accruals add to it and repayments subtract from it, the complete equation for the debt account is thus: d =−+ dt KrKrRK DdDdPD ()  (2) A second account is also  needed: a “credit” (more correctly, working capital) account  KC, into which the endogenously created money is paid by the banks. When  this account has  a positive balance, the banks are  obliged to pay interest at the rate  rc, This second account is the source from  which capitalists meet, as best they  can, their loan repayment obligations. Its equation of motion is thus: d =−+ dt KrKrRK CCCdPD ()  (3) As with the debt account, interest receipts accrue  to  KC  and principal and interest repayments subtract from it—and are instantly also deducted from  the debt account.4 Finally, accounts are needed to record the banks’ transactions. Here we note an important observation from  Graziani: in order  to prevent seigniorage, banks cannot spend the money they endogenously create, but only  the profit on the spread  between loans and deposits. We  therefore also provide two accounts for banks: a principal account  BP, into which principal repayments flow, and an income  account  BY  for banks’ lending activities. Thus  PD RK flows into the principal account: d = dt BRK PPD and the net difference between  dD 3  Solving for  R, we  get rK⋅ and  CC ln X Rr T d  (4) rK⋅ flows into the income  account: =−  where X<1. The  dr  component  represents  the  repayment of  interest on  debt;  the − ln X T  component is the repayment of  principal (this is  positive because  X<1) 4  This  is  the one sense in  which “simultaneity”  is  allowed in  this  model:  when, like  a couple kissing,  one act is the mirror image of the  other. 

Keen & Chapman 2005  Profit in a  dynamic model of the Circuit =⋅−⋅ dt BrKrK YdDcC  (5) Equations (2) to (5) complete the  model at this stage,  and encapsulate the dilemma on which all previous attempts to  explain profit in the monetary circuit have foundered: it is obvious that, at the putative end of this cycle, capitalists will make a loss. Figure 1 illustrates this with an initial loan  D0  of $1 million, a repayment target  X  of 10%, a target time  T  of 5 years, debit interest rate  rd  of 5% and a credit rate  rc  of 3%. The graphic shows the execution of this model in the mathematical simulation program Mathcad.5 5  This  model  could be implemented in  any  of  several  other packages—including  Mathematica, Maple, Matlab, Scientific  Workplace—but we find Mathcad  to have  by far the most intuitive interface. 4 of 20 

Keen & Chapman 2005  Profit in a dynamic model of the Circuit 3/19/2006 5 of 20 X10%:=T5:=rd5%:=rc3%:=D0106:=RPlnX()−T:=y10:=points1000:=GiventKDt()ddrdKDt()⋅rdRP+
⎟⎟⎟⎠t,y,points,⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦:=τ0ypoints,y..:=024681005.1051.1061.1055.10405.1041.105Capitalist DebtBankers PrincipalKC-KD Account (RHS)BY account (RHS)Capitalist DebtBankers PrincipalKC-KD Account (RHS)BY account (RHS)Transaction Account BalancesYearsKDτ()BPτ()KCτ()KDτ()−BYτ()τKCy()4.463−104×=BPy()9.9105×=KCy()KDy()−5.463−104×=BYy()5.463104×= Figure 1: Mathcad implementation of basic circuit without production or exchange Even at this simple level, our model enables us to reject an accepted Circuitist proposition, that endogenously created credit money is destroyed when debt is repaid. In his seminal paper Graziani’s states that  “As soon as firms repay their debt to the banks, the money initially created is destroyed” (Graziani 1989: 5). This belief is echoed in many subsequent Circuitist works, as Rochon documented (Rochon 2005: 126, 127, 128). It is implicit in the “Kaldor-Trevithick reflux principle” (Lavoie 1999—though it is possible to re-interpret this concept in a manner consistent with our results), and accepted widely in Post Keynesian analysis (see for example Lavoie 1992, p. 130, cited in Rochon 2005 p. 130). 

Keen & Chapman 2005  Profit in a  dynamic model of the Circuit Money is  not  destroyed when debt is repaid,  even when no income  is generated from  the borrowed money. Instead, the debt  is  paid down to (almost)  zero, while  the money that was simultaneously created with it  flows into the bankers’ principal account as an unencumbered asset. Only the failure to repay debt fully can destroy money, because then the flow back to  BP  is less than the  principal repayment required by the debt contract. The total amount of money  is conserved in this simple instance of a single injection of endogenous money, and equals (at this stage)  CP KB+.6 In a more complex model, with new credit creation, this amount would rise over time—and fall during a crisis, when insolvency and  bankruptcy destroyed more money than was newly created.  Nonetheless,  ten years  after accepting our hypothetical $1 million loan, the capitalists in our model are  still $5,463 in the red, and bankers are an equivalent amount ahead. The advantages of being a banker are  obvious: but why would anyone want to be a capitalist? Because capitalists use the working capital  KC  to finance production, sell commodities, make a profit, and repay their debts. Production  is therefore, not amazingly, an essential aspect of  the monetary theory of production. It  is this real insight of Marx’s that has become  obscured in  the  initial attempts to  come to grips  with Graziani’s monetary vision. Without a surplus generated in production, there can be no profit. A prelude:  time lags To finance production, an outflow must occur from  the capitalist working capital account. Here we introduce the systems engineering concept of a  time lag, which is a measure of the rate at which a substance flows out of a vessel—in this case, money out of the working  capital account  KC. The faster this  flow is, the more rapidly  money finances production, which in turn generates income  for capitalists  and workers. While this concept is deliberately mechanistic in this simple model,  a time lag can also be interpreted as  the aggregate outcome  of many different agents with many differing time  responses (Andresen, 1998, 1999).  In a more complex model, the lags would be a function of behavioral variables—expectations of profit, propensities to consume, etc. At this point, we use constant  time lags, since the  only question afoot is whether it is  feasible for capitalists in  the  aggregate to make a profit. Whether they do so in practice at a given time, or in a more  complete dynamic model, is another matter altogether. A time-lag differs from the discrete  time-delay  that has been a mainstay of economic reasoning, in which a variable  Y(t)  is argued to be a function of other variables at times  t-1,  t-2, etc. While most economic activities  are  discrete—wages are paid once a fortnight, cars come  off the production line one at a time, consumers buy units of commodities at discrete times, etc.—the aggregate of  many such discrete events at 6  The Kaldor-Trevithick reflux principle can be made  consistent  with  this by  treating  the balance in  BP  as  money  “not  in  circulation”, even  though  it  is  clearly  not  destroyed. 6 of 20 

uncorrelated times is better approximated by a continuous time function with a time lag than a discrete time function with a time delay. For technical reasons, the time lag is expressed as a fraction of the time unit of the model—in this case, years—and shown as an inverse in the system equations. We label the time lag for the outflow KCτ, so that the outflow from the account is 1CKCKτ.7 The essence of the circuit: financing production & profit The outflow hires workers and buys intermediate goods from other capitalists to enable the production of commodities, which are then sold to capitalists, workers and bankers. In this simple one-commodity model, all intermediate goods purchases resolve themselves into wages and profits for workers and capitalists. Thus, given production and the sale of output, the outflow 1CKCKτ generates income flows that resolve exclusively into either profits or wages. The ratio of one to the other is, in Marx’s notation, the ratio of s to v, or the rate of surplus value.8 The source of profit within the monetary circuit is thus the generation of a surplus during production, the same as it was within Marx’s abstraction of a real circuit. Given that these represent fractions of a flow that sum to 1 in our model, we express this ratio as 1ssvs=−, so that 1rsvsrsv=+ where rsv is Marx’s rate of surplus value. 1CKCsKτ− is the flow of wages. CKCsKτ is, however, not quite the flow of profits. It is instead the outflow of financial capital needed to generate the flow of profits back. Purchase of inputs, production, and sale, must all first occur, and all these processes take time. We introduce the system state F (for “factory”) to represent this process, and use τF for the related time lag between expenditure on production and income from sale. We treat production implicitly in this simple model. Our explicit model—which we are currently extending—has the inflow CKCsKτ purchasing inputs Q at price P, the production process generating output ()'1QQθ=+ with a production time lag Fτ, which is then added to stocks Θ, from which sales occur at a rate determined by the transaction time lags Fτ, Wτ and Bτ. This, however, raises issues about the time                                                  7 This is a first order time lag. We eschew more complex ones in this simple model, however higher order lags result from the interplay between the related first order differential equations. 8 Given the invalidity of the labor theory of value (Keen 2003a, 2003b, 2001), in a multi-sectoral setting, the Marxian concept of the rate of surplus value has no meaning. However in this one commodity model, it is a valid abstraction relating capitalist to worker income from production. 


dynamics of P, the consideration of which we wish to leave for a later paper.9 Our new implicit-production equation is thus: 1dCdtKCFsFKFττ=− (6) We also add the terms 1CKCKτ− and 1FFτ to the working capital account to represent, respectively, the outflows of money to finance production, and the returning lagged inflow of monetary profits. We introduce an account for workers wages WY with an inflow term of 1CKCsKτ−, and include the fact that workers accounts accrue interest cYrW; this in turn requires a matching outflow from the bankers’ income account BY. To complete the modeling of financial transactions,10 we must introduce expenditure by bankers and workers with time lags that reflect how rapidly each class must draw on its transaction account balances to fund consumption. Bankers’ and workers’ consumption spending is thus proportional to their account balances, with the ratios Bτ and Wτ respectively. There is thus an outflow from workers’ account of 1YWWτ and bankers’ account of 1YBBτ, with matching inflows into the capitalists’ account. The complete model is (with the new inflows and outflows highlighted in matching brackets):                                                  9 Since the model currently lacks an explicit concept of capital, Sraffa prices cannot be used. A simple Kaleckian markup price would be feasible, but this overrules the income distribution dynamics. We have experimented successfully with an inventory-stock pricing equation, but generally feel these issues are best left for a longer, specialized paper. 10 We emphasize that transactions and income are different concepts. The flow of the amount 1YBYBτ from bankers’ accounts to capitalists’ is a transactional flow; the portion of that which exceeds the cost of production is a flow of income to capitalists. All capitalist income flows are incorporated in 1FFτ

Keen & Chapman 2005  Profit in a dynamic model of the Circuit 3/19/2006 9 of 20 ()11-11-1111FFdDPDdtdCCCdPDdtddtdYCKCCKCCKCYWYcYcdtdPPDdtdYdDcCYBYdtYWBKsKrWrKRKKrFFBBKrRKFWBRKBrWWWKrKsKτττττττττ⎧⎫⎨⎬⎩⎭⎧⎫⎨⎬⎩⎭⎧⎡⎤
⎢⎥⎢⎥⎡⎤⎢⎥⎣⎦⎡=−=−+−++++⎢⎥⎣⎦⎢⎥⎣⎤⎢⎥⎣==−==⋅−⋅+−⎫⎨⎬⎩⎭⎦⎦⎡⎤⎢⎥⎢⎥ (7) Figure 2 shows the results of a simulation of this model over a 20 year time period, with the additional parameter values of 14KCFττ==,2Bτ=, 126Wτ= and 200%rsv= (corresponding to an s value of 0.667). The top graph shows the account dynamics over the full twenty years; the bottom graph highlights the second and third order dynamics that occur in the first three years of the simulation. In contrast to the previous incomplete model, capitalist indebtedness tapers to zero—as do all income accounts. Capitalists have been able to borrow money, produce output, sell it, repay debt, and make a profit. 

Keen & Chapman 2005  Profit in a  dynamic model of the Circuit 1.106 5.105 4.104 2.104 0 Capitalist Debt Bankers Principal KC+F-KD (RHS) Capitalist Debt Bankers Principal KC+F-KD (RHS) 0 BY (RHS) WY (RHS) BY (RHS) WY (RHS) 2.104 4.104 02468101214161820 1.106 5.105 4.104 02 Capitalist Debt Capitalist Debt Bankers Principal Bankers Principal KC+F - KD (RHS) KC+F - KD (RHS) 0 0 0.5 1 1.5 2 Figure  2:  Transaction  account  dynamics without  relending BY (RHS) WY (RHS) BY (RHS) WY (RHS) 2.5 3 .104 2.104 4.104 Figure 3  shows the associated income  flows, and the aggregate income  levels generated by  the model. These are, respectively: 

Keen & Chapman 2005  Profit in a  dynamic model of the Circuit y Net  Profits: y Wages: ∫ ∫ 0 11 ⎛⎞ ⎜⎟ τ F FrKdt −⋅ ⋅ dD ⎝⎠ 0 τ s Kdt C KC Bank  Income: ∫ y 0 ⋅ rKrKrWdt ⋅−⋅− ⋅ () dDcCcY  (8) The first two are the Circuitist versions  of  Kalecki’s classic statement that “capitalists get what they spend,  workers spend what they get”.11  The third adds  the component that neither Keynes nor Kalecki  properly incorporated, bank profits from finance—“bankers interest what they  lend”. In this debt-finance only model, ∫ 1 τ F −⋅ dD FrK is the  M+  of  Marx’s monetary  circuit; the  M  is  solely the servicing costs of their debt  because, in  the absence of equity finance, capitalists advance no money of their own. In the incomplete model, bankers were the clear winners and  capitalists the losers. In this complete model, however, “everybody wins”, though  capitalists more so than workers (given the assumed rate of surplus value), and bankers least of  all. 11  Workers’ and capitalists’ incomes include  interest on their credit balances, so  that aggregate income  sums  to  wages  plus  profits  plus interest  on  outstanding  debt. The  term  y  in  the integration limit  is the number  of  years in  the simulation—in this case, 20. 11 of 20 

Keen & Chapman 2005  Profit in a  dynamic model of the Circuit 2.106 1.5 .106 1.106 5.105 0 4.104 3.104 2.104 1.104 Flow of profit Flow of profit Flow of wages Flow of wages 1.5 .106 Aggregate profit (RHS) Aggregate profit (RHS) Aggregate wages (RHS) Aggregate wages (RHS) 1.106 5.105 0 012345678910 1.105 8.104 6.104 4.104 Flow Bank Income Aggregate Bank Income (RHS) Flow Bank Income Aggregate Bank Income (RHS) 0 2.104 0 012345678910 Figure  3: Income dynamics without  relending The magnitude and dynamics  of  profit and income distribution This model  indicates other determinants of profit considered by Marx, but neglected until now in Circuitist  thinking: the rate of turnover  of financial capital, and the speed of the process of production.  KC τ financial capital;  F  determines how quickly  capitalists employ their τ  determines how quickly production and sale turns inputs into outputs and then profits. The faster both  these processes  are, the more  income  that is generated in production per unit of time—and the more quickly capitalists repay their debts to bankers. A fall in either  of  these time lags thus increases capitalist and worker incomes and reduces bankers’, as shown in Figure 4. For a sufficiently small time  lag—under 1/6th of  a year in these simulations—the  profits earned  in this model can exceed the size of  the original loan. In general, profits far exceed  the interest  payments necessitated by the loan, even with a production lag of one year.  Clearly, as Minsky once observed in another context, “it pays to lever”. 12 of 20 

Keen & Chapman 2005  Profit in a dynamic model of the Circuit 3/19/2006 13 of 20 
Figure 4: Income distribution vs time lags in production The time pattern of relative income flows also bears noting. As Figure 5 shows, given our base simulation with 14KCFττ==, capitalist income starts well below both worker and banker income. However, by the end of the simulation, aggregate profits are precisely twice aggregate wages (equivalent to the rate of surplus value of 200%), while aggregate profits exceed aggregate bank income by a factor of more than 15. 0246810121416182000.511.5205101520

The non-destruction of money One final point deserves emphasis here: the conservation of money in this simple model without re-lending, and,  in capitalism  in  general,  the non-destruction of money except via bankruptcy. The top graph in Figure 6 plots the sum  of all income  accounts plus bankers’ principal: this is identically equal to the original injection of endogenous money. Aggregate account balances + KC τ() F τ() ... ... + + + WY τ() BY τ() BP τ() ... ... 1.106 9.99999999999.105 1.106 ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ + KC τ() F τ() ... ... + + + WY τ() BY τ() BP τ() ⎞ ... ⎟ ⎟ ⎟ ⎟ ... ⎟ ⎠ − KD τ() 5.105 0 5 10 τ 15 Aggregate bank balances minus capitalist debt 20 0 0 5 10 τ 15 Aggregate capitalist debt and bankers' principal 1.106 9.99999999999.105 20 0 5 Figure 6:  the non-destruction of  money 10 15 20 The middle graph shows that what is destroyed by debt repayment is simply debt. As the impulse from  the original injection of endogenous money dies out, all the endogenous money accumulates in the bankers’ principal account, while  capitalist debt is paid down to zero. 

The final graph establishes another identity: the sum  of  bankers’ principal and capitalist debt represents  the net assets of bankers, which is identical to the initial creation of endogenous money. Perpetuating the circuit: re-lending of bankers’ principal The model as specified above decides two issues that have remained in contention amongst Circuitists for some  time: money is  not destroyed by debt repayment; and a profit can be earned on borrowed money. However,  it cannot yet address a third area of debate: whether economic activity can be sustained without new injections of money. Contrary to Fontana (2000), Andresen  (2006) answers this  question in the affirmative. We consider this issue by allowing for re-lending of bankers’ principal  BP. Again, we model this with a simple time lag  τBP., where  in this simulation τ =  This is added as new debt to the capitalists’ debit account, and  new working capital to the credit account. Our complete model of financial flows is thus (with the new elements highlighted by  matching brackets): BP d dt d dt d dt d dt d dt d KRK =− + 1 ⎧⎫ DPD τ B ⎨⎬ P BP ⎩⎭ () 1111 KrKrRK K FW B ⎧ ⎨ 1 =−+−++++ CCCdPD C Y Y KC ττττ F s 1 =− FKF C KC ττ 1s F 1 =+− WKrWW YCcYY KC ττ W BRK 1 =− PPD W B τ ⎩ ⎧⎫ τ B ⎨⎬ P BP ⎩⎭ BrKrKrW d t 1 =⋅−⋅+ − B YdDcCcY Y τ B B BP ⎫ P ⎬ ⎭ 4  (9) As Figures 6 and 7 show,  our modeling concurs with  Andresen’s: this model economy can function at a sustained level  with only a single injection of endogenous money. Economic activity continues  because, rather than all the money accumulating in the bankers’ principal account, a proportion of  it continues to be lent, renewing the supply of circulating money, and hence  production and the generation of income. 

Figure  7:  Sustained economic  activity  with  relending of  bank  principal 2.5 3 .104 2.104 4.104 6.104 Figure 8 confirms  that the circulation of  this fixed amount of money generates a continuous stream  of income  for all three classes in the model: 

Figure  8:  Sustained income  flows  with re-lending Flow of profit Flow of wages Flow of profit Flow of wages Aggregate profit (RHS) Aggregate profit (RHS) Aggregate wages (RHS) Aggregate wages (RHS) 6.106 4.106 2.106 0 012345678910 4.105 3.105 2.105 Flow Bank Income Flow Bank Income Aggregate Bank Income (RHS) Aggregate Bank Income (RHS) 1.105 0 012345678910

Re-lending of principal only slightly alters the time pattern  of aggregate income flows.12  As Figure 9 shows, the capitalist: worker  income  ratio  does not quite reach  the rate of  surplus value. The Profit:Bankers’ income ratio, on the other  hand, now tapers  to 15.608—only slightly more than the 15.549 ratio that applied without re-lending. 12  Aggregate income  for a  class  at time  t  is the integral of the  income  from  zero years to  t. 

Figure  9:  Ratio  of  aggregate  incomes  over  time with re-lending Profit:Wages Profit:Wages Profit:Bank (RHS) Profit:Bank (RHS) 0 5 10 Years 15 From Circuitist skeleton to the body economic 20 15 10 5 0 20 Profit: Bank Income Ratio This is a deliberately skeletal model, designed only to show that the monetary circuit is internally consistent, and  that it can  explain both the endogeneity of  credit money, and the phenomenon of monetary profit. In a full Circuitist model, new injections of money would be occurring all the time; flows between accounts would be determined by behavioral relations rather than fixed  parameters; production would be multi-sectoral; prices and the distribution of income  would  be changing continuously; profits would rise and fall, and uncertainty about the future  would lead to booms, slumps, bubbles, depressions,  exceeded and dashed  expectations, bankruptcy, and  all the panoply of everyday actual capitalism. We hope that, in providing this skeleton,  we have enabled Circuitist thinking to transcend some  early conundrums. We invite other Circuitists to join us  in putting flesh on this skeleton. References Andresen, Trond, (1998), “The macroeconomy as a network of money-flow transfer functions”,  Modeling, Identification, and Control, 19, p. 207-223. Andresen, Trond, (1999), “The Dynamics of Long-range Financial Accumulation and Crisis”,  Nonlinear Dynamics, Psychology, and Life Sciences, 3, pp. 161-96. Andresen, Trond, (2006), “A critique of a  Post Keynesian model of hoarding, and an alternative model”,  Journal of Economic Behavior & Organization  (forthcoming). Bellofiore, Riccardo., Davanzati, G. F.  and Realfonzo, R, (2000), “Marx inside the Circuit: Discipline Device, Wage Bargaining and Unemployment in a Sequential Monetary Economy”,  Review of Political Economy, 12, pp. 403-17. 

Keen & Chapman 2005  Profit in a  dynamic model of the Circuit Fontana, Guiseppe., 2000. “Post Keynesians and Circuitists on money and uncertainty: an attempt at generality”,  Journal Of Post Keynesian Economics, 23, pp. 2748. Fontana, Giuseppe, (2003), Post Keynesian Approaches to endogenous money: a time framework explanation,  Review of Political Economy, 15, pp. 291-314 Fontana, Guiseppe, (2004), “Hicks on monetary theory and history: money as endogenous  money”,  Cambridge Journal of Economics, 28, pp.  73-88. Fontana, Giuseppe  and Venturino, Ezio, (2003), Endogenous money: an analytical approach,  Scottish Journal of Political Economy, 50, pp. 398-416 Fontana, Guiseppe, & Realfonzo, R., (eds.), (2005),  The Monetary Theory of Production, Palgrave, New York. Graziani, Augusto, (1989). “The Theory of the Monetary Circuit”,  Thames Papers in Political Economy, Spring,:1-26. Reprinted in Musella, M. & Panico, C., (eds.),   (1995),  The Money Supply in the Economic Process, Edward Elgar,Aldershot. Keen, Steve, (1993a). "Use-value, exchange-value, and the demise of Marx's labor theory of value",  Journal of the History of Economic Thought, 15, pp. 107-121. Keen, Steve, (1993b). "The misinterpretation of Marx's  theory of value",  Journal of the History of Economic Thought, 15, pp. 282-300. Keen, Steve, (2001). "Minsky's thesis: Keynesian or Marxian?" in Bellofiori, R., & Ferri, P., (eds.),  Financial Keynesianism and Market Instability,  Edward Elgar, Aldershot. Lavoie, Marc (1992),  Foundations of Post Keynesian Economic Analysis, Edward Elgar, Aldershot. Lavoie, Marc, (1996),  “Horizontalism, Structuralism,  liquidity  preference and the principle of increasing risk”,  Scottish Journal of Political Economy, 43, pp. 275-300. Lavoie, Marc, (1999), “The credit-led  supply of deposits  and the demand for money: Kaldor’s reflux mechanism as  previously endorsed by Joan Robinson”, Cambridge Journal of Economics, 23, pp. 103-113. Marx, Karl, (1951 [1865]), “Wages, price and profit” in  Marx-Engels Selected Works , Volume I, Marx-Engels-Lenin Institute (ed.), Foreign Languages Publishing House, Moscow. Marx, Karl, (1954 [1867]),  Capital Vol. I, Progress Publishers, Moscow. Messori, Marcello & Zazzaro, A., (2005)  “Single-period  analysis: financial markets, firms’ failures  and closure of the  monetary  circuit”, in  Fontana & Realfonzo (2005), pp. 111-123. Rochon, Louis-Philippe, (2005), “The existence of monetary profits within the monetary circuit”, in Fontana & Realfonzo (2005), pp. 125-138. 

Keen & Chapman 2005  Profit in a  dynamic model of the Circuit i  We  thank  Trond  Andresen, of  the Norwegian University  of Technology, for  numerous illuminating  discussions and  practical suggestions  in  the development of  this model.